Pion-pion phase shifts from covariant perturbation theory for a chiral invariant field theoretic model

The Lehmann model for pion-pion scattering consists of a low-energy expansion of the scattering amplitude to fourth order in the momenta on the basis of the chiral-invariant pion-nucleon Lagrangian. Because of the non-renormalizability of the pion Lagrangian two parameters remain undetermined in the pion-loop contribution. Using covariant perturbation theory and superpropagator methods the authors calculate these two parameters independently of the choice of the pion field coordinates. The resulting phase shifts are shown to be in very good agreement with the data. (17 refs).